Sliding mode control for a class of time-delay hybrid linear systems with mismatched Markovian jump parameter

The sliding mode control problem of a class of uncertain time-delay hybrid linear systems with mismatched Markovian jump parameter is considered. Under the assumptions of known upper bounds mismatched system uncertainties, the sufficient conditions is proposed to guarantee the mean exponentially stability of reduced-order sliding mode system. Under the condition of mismatched system uncertainties, robust sliding mode control law is proposed. The control methods guarantees that the trajectory of system arrives at the sliding surface in finite time interval and is kept here thereafter. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of linear matrix inequalities(LMIs) have solution. Lastly a simulation is given to illustrate the effectiveness of the proposed approach.